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Johannes Kepler (1571-1630) did extensive calculations involving careful observations that astronomer Tycho Brahe had made of the motion of Mars. Eventually he realized that Mars was moving around the sun in an elliptical orbit rather than a circular one. He correctly deduced that the orbits of the other planets are elliptical also. Kepler believed that there was a force in the Earth that caused the motion of the moon.
Galileo (1564 - 1642) cleverly used ramps to slow down the effects of gravity. This way he could study moving objects and time their motion carefully. He quickly realized that the smoothness of the ramps was important to minimize the effect of friction, and he correctly concluded that a moving object would keep moving forever if there was no friction. His experiments showed that a heavy object falls just as fast as a lighter object if there is no air resistance.
Galileo's ramp experiments showed that a falling object falls faster and faster, and the distance traveled is related to the square of the time.
Isaac Newton (1642 - 1726) discovered that the force of gravity that causes an apple to fall from a tree is the same force that holds the moon in orbit. In Newton's day a popular explanation for the motion of the planets was that they moved due to swirls in the celestial aether, but Newton showed that the force of gravity was responsible. He developed mathematical methods that allowed him to calculate that the planets move in elliptical orbits, and to explain that the distance traveled by a falling object must be related to the square of the time.